Keynesian Models by Orthodox Keynesians Keynesian Cross Samuelson

<Keynesian> Models by Orthodox Keynesians • Keynesian Cross Samuelson [Dorbusch et al, 2008: Chapter 9] * IS-LM Model Hicks, …, MF [Dorbusch et al, 2008: Chapters 10 -12]

Keynesian Cross

Ch. 9 INCOME & SPENDING (Dorbusch et al, 2008) • • Introduction One of the central questions in macroeconomics is why output fluctuates around its potential level • • This chapter offers a first theory of these fluctuations in real output relative to trend • • In business cycle booms and recessions, output rises and falls relative to the trend of potential output Cornerstone of this model is the mutual interaction between output and spending: spending determines output and income, but output and income also determine spending The Keynesian model of income determination develops theory of AD • Assume that prices do not change at all and that firms are willing to sell any amount of output at the given level of prices AS curve is flat 9 -3

AD and Equilibrium Output • • AD is the total amount of goods demanded in the economy: (1) Output is at its equilibrium level when the quantity of output produced is equal to the quantity demanded, or (2) • When AD is not equal to output there is unplanned inventory investment or disinvestment: (3), where IU is unplanned additions to inventory • If IU > 0, firms cut back on production until output and AD are again in equilibrium 9 -4

The Consumption Function in V. Simple Model [No Gov’t & F. Trade] • Consumption is the largest component of AD • Consumption is not constant, but increases with income the relationship between consumption and income is described by the consumption function • If C is consumption and Y is income, the consumption function is • • (4), where and The intercept of equation (4) is the level of consumption when income is zero this is greater than zero since there is a subsistence level of consumption The slope of equation (4) is known as the marginal propensity to consume (MPC) the increase in consumption per unit increase in income 9 -5

The Consumption Function & AD in V. Simple Model [No Gov’t & F. Trade] [Insert Figure 9 -1 here] 9 -6

The Formula for Equilibrium Output • Can solve for the equilibrium level of output, Y 0, algebraically: • • • The equilibrium condition is Y = AD Substituting (AD= ) into EQ. yields Solve for Y to find the equilibrium level of output: The equilibrium level of output is higher the larger the MPC and the higher the level of autonomous spending. 9 -7

Consumption and Savings • Income is either spent or saved a theory that explains consumption is equivalently explaining the behavior of saving • • More formally, (5) a budget constraint Combining (4) and (5) yields the savings function: (6) • Saving is an increasing function of the level of income because the marginal propensity to save (MPS), s = 1 -c, is positive • • Savings increases as income rises Ex. If MPS is 0. 1, for every extra dollar of income, savings increases by $0. 10 OR consumers save 10% of an extra dollar of income 9 -8

Your Turn Consider the following model: a. Derive the AD equation. b. Find the equilibrium level of output. c. Derive the autonomous spending multiplier.

Consumption, AD, and Autonomous Spending: Extended Model • Now we incorporate the other components of AD: G, I, taxes, and foreign trade (assumed as autonomous) • • Consumption now depends on disposable income, (7) and (8) AD then becomes (9) where A is independent of the level of income, or autonomous 9 -10

Consumption, AD, and Autonomous Spending [Insert Figure 9 -2 here] 9 -11

Equilibrium Income and Output • • Equilibrium occurs where Y=AD, which is illustrated by the 45° line in Figure 9 -2 point E The arrows in Figure 9 -2 show the economy reaches equilibrium • • At any level of output below Y 0, firms’ inventories decline, and they increase production At any level of output above Y 0, firms’ inventories increase, and they decrease production Process continues until reach Y 0 9 -12

The Formula for Equilibrium Output Déjà vu • Can solve for the equilibrium level of output, Y 0, algebraically: • • • The equilibrium condition is Y = AD (10) Substituting (9) into (10) yields (11) Solve for Y to find the equilibrium level of output: (12) The equilibrium level of output is higher the larger the MPC and the higher the level of autonomous spending. 9 -13

The Formula for Equilibrium Output • Equation (12) shows the level of output as a function of the MPC and A • • Frequently we are interested in knowing how a change in some component of autonomous spending would change output Relate changes in output to changes in autonomous spending through (13) • Ex. If the MPC = 0. 9, then 1/(1 -c) = 10 an increase in government spending by $1 billion results in an increase in output by $10 billion • Recipients of increased government spending increase their own spending, the recipients of that spending increase their spending and so on 9 -14

Saving and Investment • In equilibrium, planned investment equals saving in an economy with no government or trade • • [Insert Figure 9 -2 here again] In figure 9 -2, the vertical distance between the AD and consumption schedules is equal to planned investment spending, I The vertical distance between the consumption schedule and the 45° line measures saving at each level of income at Y 0 the two vertical distances are equal and S = I 9 -15

The Multiplier • By how much does a $1 increase in autonomous spending raise the equilibrium level of income? The answer is not $1 • • Out of an additional dollar in income, $c is consumed Output increases to meet this increased expenditure, making the total change in output (1+c) The expansion in output and income, will result in further increases process continues. The steps in the process are shown in Table 9 -1. The general definition of the multiplier is the amount by which equilibrium output changes when autonomous aggregate demand increases by 1 unit [Insert Table 9 -1 here] • If we write out the successive rounds of increased spending, starting with the initial increase in autonomous demand, we have: (15) • This is a geometric series, where c < 1, that simplifies to: • (16) 9 -16

The Multiplier • Figure 9 -3 provides a graphical interpretation of the effects of an increase in autonomous spending on the equilibrium level of output • • • [Insert Figure 9 -3 here] The initial equilibrium is at point E, with income at Y 0 If autonomous spending increases, the AD curve shifts up by , and income increases to Y’ The new equilibrium is at E’ with income at 9 -17

The Government Sector: now TA=t. Y The government affects the level of equilibrium output in two ways: • 1. 2. Government expenditures (component of AD) Taxes and transfers Fiscal policy is the policy of the government with regards to G, TR, and TA • • • Assume G and TR are constant, and that there is a proportional income tax (t) The consumption function becomes: (19) The MPC out of income becomes c(1 -t) 9 -18

The Government Sector: • Combining (19) with AD: (20) • Using the equilibrium condition, Y=AD, and equation (19), the equilibrium level of output is: (21) • The presence of the government sector flattens the AD curve and reduces the multiplier to 9 -19

Income Taxes as an Automatic Stabilizer • Automatic stabilizer is any mechanism in the economy that automatically (without case-by-case government intervention) reduces the amount by which output changes in response to a change in autonomous demand • • One explanation of the business cycle is that it is caused by shifts in autonomous demand, especially investment Swings in investment demand have a smaller effect on output when automatic stabilizers are in place (ex. Proportional income tax) • Unemployment benefits are another example of an automatic stabilizer enables unemployed to continue consuming even though they do not have a job 9 -20

Effects of a Change in Fiscal Policy • Suppose government expenditures increase • • • [Insert Figure 9 -3 here] Results in a change in autonomous spending and shifts the AD schedule upward by the amount of that change At the initial level of output, Y 0, the demand for goods > output, and firms increase production until reach new equilibrium (E’) How much does income expand? The change in equilibrium income is (22) 9 -21

Effects of a Change in Fiscal Policy (22) • [Insert Figure 9 -3 here] A $1 increase in G will lead to an increase in income in excess of a dollar If c = 0. 80 and t = 0. 25, the multiplier is 2. 5 A $1 increase in G results in an increase in equilibrium income of $2. 50 G and Y shown in Figure 9 -3 • Expansionary fiscal policy measure 9 -22

Effects of a Change in Fiscal Policy • Suppose government increases TR instead • • Autonomous spending would increase by only c TR, so output would increase by G c TR The multiplier for transfer payments is smaller than that for G by a factor of c • • Part of any increase in TR is saved (since considered income) If the government increases marginal tax rates, two things happen: • • The direct effect is that AD is reduced since disposable income decreases, and thus consumption falls The multiplier is smaller, and the shock will have a smaller effect on AD 9 -23